Clipping Outliers: NYC hotel pricing dataset analysis

Sometimes, while analyzing a dataset, there can be some data present which might exert undue influence while building models, like linear regression. These data are called outliers. Outliers can sometimes mislead the set of data and influence model performance as well.

What are outliers?

In data science, outliers are values within a dataset that vary greatly from the others, they are either much larger, or significantly smaller. Outliers can appear in a dataset due to variability of measurement, error in data, experimental error etc. Outliers can cause machine learning models to make inaccurate predictions when they are included in the training data, so they need to be handled before training a model.

One of the best ways to understand outliers is box plots.

Boxplots are very useful to see the distribution of a variable/feature and detect outliers in them. It is a useful graphical representation for describing the behavior of the data in the middle as well as both ends of the distribution. A box plot shows the data based on the five-number summary: the minimum(Q0), the first(Q1) quartertile, the sample median(Q2), the third quartile(Q3) and the maximum(Q4).

• Minimum: the lowest data point in a variable excluding any outliers
• Median (Q2 or 50th percentile): the middle value in the variable
• First quartile (Q1 or 25th percentile): also known as the lower quartile (0.25)
• Third quartile (Q3 or 75th percentile): also known as the upper quartile (0.75)
• Maximum: the highest data point in the variable excluding any outliers

The difference between the lower quartile and the upper quartile(Q3 - Q1) is called the interquartile range or IQR.

Boxplots help us find the outliers in the data by using the IQR. As a rule, values that are outside the range of 1.5*IQR from Q1 and Q3 are regarded as outliers. The below image will help us better understand the outliers in our data.

In the image above, the points that are outside the whisker lines are the outliers.

There are different techniques to handle outliers in a dataset. In our example, we will use the concept of clipping (winsorizing).

What is winsorizing/clipping?

Clipping data from a dataset means to clip the data at the last permitted extreme value, e.g. the 5th or 95th percentile value. For example, when we clip the data to 95th percentile, values over the 95th percentile will be set to the 95th percentile value meaning all the values greater than 95% percent will equal to the 95th percentile value.

The following data set has several (bolded) extremes:

• {0.1, 1, 12, 14, 16, 18, 19, 21, 24, 26, 29, 32, 33, 35, 39, 40, 41, 44, 99, 125}

After clipping/winsorizing the top and bottom 10% of the data(matching those values to the nearest extreme), we get:

• {12, 12,12, 14, 16, 18, 19, 21, 24, 26, 29, 32, 33, 35, 39, 40, 41, 44, 44, 44}

Let us solve a problem that removes outliers from data using clipping.

Problem Description

For illustration of the clipping method, lets look at an example.

We have a dataset named nyc_airbnb.csv , which contains data about price of AirBnb per-night rental houses. In the dataset, there exists some outliers in the price variable. Our task is to find out the outliers and remove them by winsorizing/clipping.

First , we load our dataset into a dataframe and view it.

Load the Dataset and View data

The steps are:

• import the pandas library as pd
• load the data into a variable nyc using read_csv method in pandas
• view the variable nyc.

import pandas as pd
nyc= pd.read_csv("../datasets/nyc_airbnb.csv")

nyc

	id	name	host_id	host_name	neighbourhood_group	neighbourhood	latitude	longitude	room_type	price	minimum_nights	number_of_reviews	last_review	reviews_per_month	calculated_host_listings_count	availability_365
0	2539	Clean & quiet apt home by the park	2787	John	Brooklyn	Kensington	40.64749	-73.97237	Private room	149	1	9	2018-10-19	0.21	6	365
1	2595	Skylit Midtown Castle	2845	Jennifer	Manhattan	Midtown	40.75362	-73.98377	Entire home/apt	225	1	45	2019-05-21	0.38	2	355
2	3647	THE VILLAGE OF HARLEM....NEW YORK !	4632	Elisabeth	Manhattan	Harlem	40.80902	-73.94190	Private room	150	3	0	NaN	NaN	1	365
3	3831	Cozy Entire Floor of Brownstone	4869	LisaRoxanne	Brooklyn	Clinton Hill	40.68514	-73.95976	Entire home/apt	89	1	270	2019-07-05	4.64	1	194
4	5022	Entire Apt: Spacious Studio/Loft by central park	7192	Laura	Manhattan	East Harlem	40.79851	-73.94399	Entire home/apt	80	10	9	2018-11-19	0.10	1	0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
48890	36484665	Charming one bedroom - newly renovated rowhouse	8232441	Sabrina	Brooklyn	Bedford-Stuyvesant	40.67853	-73.94995	Private room	70	2	0	NaN	NaN	2	9
48891	36485057	Affordable room in Bushwick/East Williamsburg	6570630	Marisol	Brooklyn	Bushwick	40.70184	-73.93317	Private room	40	4	0	NaN	NaN	2	36
48892	36485431	Sunny Studio at Historical Neighborhood	23492952	Ilgar & Aysel	Manhattan	Harlem	40.81475	-73.94867	Entire home/apt	115	10	0	NaN	NaN	1	27
48893	36485609	43rd St. Time Square-cozy single bed	30985759	Taz	Manhattan	Hell's Kitchen	40.75751	-73.99112	Shared room	55	1	0	NaN	NaN	6	2
48894	36487245	Trendy duplex in the very heart of Hell's Kitchen	68119814	Christophe	Manhattan	Hell's Kitchen	40.76404	-73.98933	Private room	90	7	0	NaN	NaN	1	23

48895 rows × 16 columns

Check for outliers in price data

Since we are looking to find out the outliers in the hotel price , an effective way of finding outliers is using visualizations. To see where the outliers lie in price data, strip plot is a very useful graph to see how the datapoints are spread.

Plot a strip plot for outlier estimation:

For our strip plot, we visualize every datapoint of the price data. We look at the spread of price data in the y axis. For this plot, we import the plotly express library.

The steps are:

• import the plotly.express library as px
• using px, call the strip() method to generate the strip plot
• inside the method, the parameters will be,
  • nyc: variable where the data is stored
  • price: column data to plot in the y axis
• store the result into a variable price_strip that will save the plot in this variable
• display the variable price_strip using the show() method

import plotly.express as px
import plotly.io as pio

pio.renderers.default = "plotly_mimetype+notebook"

price_strip = px.strip(nyc, y='price')

price_strip.show()

From the strip plot, we can see that the data range is between 0-10,000. The majority of the datapoints are within the range of 0-2000 and a few of them are over 4000. We can see that there definitely exists some outliers in the price data. The points beyond them (> 4000) can be considered as outliers for price data. But we need to know the exact outlier points to apply clipping to the data.

Let us plot a boxplot on the price data and compare it to the boxplot explained above.

The steps are:

• call the boxplot() method to generate the boxplot
• inside the method, the parameters will be,
  • column: the column data to plot for the boxplot
  • figsize(optional): to define the size of the figure in terms of width and height
  • fontsize(optional): to show the texts size in the figure
  • vert(optional): the allignment(x or y axis) of the plot. Value False means horizontal(x axis) alignment, True vertical alignment
• apply the boxplot() method to the variable nyc, where our data is stored
• store the result in a variable box_price
• use the box_price variable to display the boxplot

box_price = nyc.boxplot(column='price',figsize=(10,5), fontsize='8', vert=False)

box_price

<AxesSubplot:>

From the boxplot, we can see that most of the datapoints are outside the whisker lines (on the right side, these are actually the outliers). The valid range of values (that are not outliers) would be within the whisker points (range of Q1-1.5IQR and Q3 + 1.5IQR). The datapoints outside this range are the outlier points.

Our task now is to find these limit points to remove the outliers.

Use describe() for price distribution in terms of numbers:

To find the exact non-outlier points range in price, we need to see the number distribution of price in the quartile division. This will give us a better understanding of where the outliers lie. We will use the describe method to know about the distribution of price data.

The steps are:

• select the price column from the variable nyc
• use the describe() method on the price data. This will show the price data distribution on the five number summary

nyc['price'].describe()

count    48895.000000
mean       152.720687
std        240.154170
min          0.000000
25%         69.000000
50%        106.000000
75%        175.000000
max      10000.000000
Name: price, dtype: float64

Here, if we look on the price distribution, we can see the min, 25%, 50%, 75% and max price value of price. The price values ranges from 0 to 10000 and the 75% percentile value of price is 175. This means 75% price value is within 0 -175. So, lots of datapoints are in the 75-100% range . Our outliers lie mostly in this region of values.

Find the Outliers:

Using the quantile formula, we find out our interquartile(IQR) range alongside lower and upper limits for outlier points. For that , we find out the q3 and q1 points in the price data.

Calculate Q3:

The q3 point is the data point that represents the 75th percentile value in the price data.

The steps are:

• select the price column from the variable nyc
• use the quantile() method on the price data
• inside the quantile method, the parameter will be,
  • the percentile value whose datapoint we want to find(75% for q3)
• store the result in a variable q3
• print the variable q3

q3= nyc['price'].quantile(0.75)

print("q3:",q3)

q3: 175.0

Calculate Q1:

Similar to q3,the q1 data point represents the 25th percentile value of price data.

The steps are:

• select the price column from the variable nyc
• use the quantile() method on the price data
• inside the quantile method, the parameter will be,
  • the percentile value whose datapoint we want to find(25% for q1)
• store the result in a variable q1
• print the variable q1

q1= nyc['price'].quantile(0.25)

print("q1:",q1)

q1: 69.0

Find the interquartile range (IQR):

After calculating q1 and q3, we find out the interquartile range which is the difference between these two points. This range will determine the outlier points(upper and lower bound) for our price data.

The steps are:

• substract q3 from q1
• store the result in a variable iqr
• print the variable iqr

iqr= q3 - q1

print("iqr:",iqr)

iqr: 106.0

Calculate the upper and lower bound for outliers:

After finding the interquartile range(iqr), the next task is to calculate the upper and lower bound points to find out the outlier range in the data. We use the iqr and the calculated q1,q3 data points to find out the lower and upper bound points.

For the lower bound, the point will be 1.5*iqr from q1 which means (q1 - 1.5*iqr)

For the upper bound, the point will be 1.5*iqr from q3 which means (q3 + 1.5*iqr)

The steps are:

for upper bound,

• define the range q3 + 1.5*iqr
• store it in a variable upper_bound
• print the upper_bound

for lower bound,

• define the range q1 - 1.5*iqr
• store it in a variable lower_bound
• print the lower_bound

upper_bound= q3 + 1.5*iqr

print("upper bound",upper_bound)

lower_bound= q1 - 1.5*iqr

print("lower bound",lower_bound)

upper bound 334.0
lower bound -90.0

Clip the Outliers:

Find the Clipping points:

Now that we have found the outlier points, we need to clip the price data according to those points. The clipping points for the upper and lower bound will be as follows:

• lower_point= max(lower_bound, nyc['price'].min())
• upper_point= min(upper_bound, nyc['price'].max())

For lower point of outliers, we are actually taking the max value between the minimum price value (0) and the lower_bound because we can go as far as the minimum data point that we have. In this example, we found that our lower_bound is -90. But our lowest data point is 0. So we dont need the lower bound as -90. We need to go only as far as the lowest data point that is 0.

The same stands for the upper bound data. We need to go only as far as the highest datapoint. The maximum datapoint we have is 10,000 and our lower bound is 334. So we will take the minimum from these two points.

That is why we are using this min() for upper point and max() for lower bound calculation.

The steps are:

for lower_point,

• use the max() function
• the function parameters will be,
  • lower_bound: calculated in the previous step
  • nyc['price'].min() : the minimum value in the nyc['price'] data
• store that function into variable lower_point
• print the variable lower_point

for upper_point,

• use the min() function
• the function parameters will be,
  • upper_bound: calculated in the previous step
  • nyc['price'].max() : the maximum value in the nyc['price'] data
• store that function into variable upper_point
• print the variable upper_point

lower_point= max(lower_bound, nyc['price'].min())

print("lower_point", lower_point)

upper_point= min(upper_bound, nyc['price'].max())

print("upper_point", upper_point)

lower_point 0
upper_point 334.0

Clip outliers using the clipping points:

Now that we have found our lower and upper point, we clip our data according to them.After clipping, as shown in our introductory example, the points less than the lower_point will be set to the lower_point and the points greater than the upper point will be set to the upper_point. By doing this , it will remove the outlier points from the price data. This method of removing outliers from data is called winsorizing.

The steps are:

• select the price column from nyc dataframe
• call the clip() method on the price column
• in the method, set the parameters as,
  • lower_point: the lower point of price data
  • upper_point: the upper point of price data
• set the result to the price column of nyc dataframe to make the changes permanent

nyc['price'] = nyc['price'].clip(lower_point, upper_point)

Check final clipped data:

After clipping, We check the five number summary of price data using the describe method.

The steps are:

• select the price column from the variable nyc
• use the describe() method on the price data

nyc['price'].describe()

count    48895.000000
mean       132.979753
std         83.530504
min          0.000000
25%         69.000000
50%        106.000000
75%        175.000000
max        334.000000
Name: price, dtype: float64

After clipping the price data, we can see the distribution has become more dense (0-334) which was in the range(0-10000) before. Building a model from the new price distribution now will give us a better estimation of hotel prices since all the outlier values are removed from it.

Distribution after clipping data

Let us see how our strip plot looks now compared to the intial one we plotted and see the difference.

The steps are:

• using px, call the strip() method to generate the strip plot
• inside the method, the parameters will be,
  • nyc: variable where the data is stored
  • price: column data to plot in the y axis
• store the result into a variable price_strip2 that will save the plot in this variable
• display the variable price_strip2 using the show() method

price_strip2= px.strip(nyc, y='price')

price_strip2.show()

Now lets visualize the boxplot to check if outliers exist in the price data.

The steps are:

• call the boxplot() method to generate the boxplot
• inside the method, the parameters will be,
  • column: the column data to plot for the boxplot
  • figsize(optional): to define the size of the figure in terms of rows and columns
  • fontsize(optional): to show the texts size in the figure
  • vert(optional): the allignment(x or y axis) of the plot. Value False means horizontal(x axis) alignment, True vertical alignment
• apply the boxplot() method to the variable nyc, where our data is stored
• store the result in a variable box_price2
• use the box_price2 variable to display the boxplot

box_price2= nyc.boxplot(column='price', figsize=(10,5), fontsize='8', vert=False)
box_price2

<AxesSubplot:>

From the image above, we can see that there are no outlier points (dotted points) beyond the whisker marks which indicates that the outliers points have been removed by clipping/winsorizing.

Conclusion

By using the clip method, we have removed our outliers from the price data. Now using this dataset will give us good predictions of airbnb hotel prices in New York.